Related papers: Ab Initio Generalized Langevin Equation

For reproducing the anomalous -- i.e., sub- or super-diffusive -- behavior in some stochastic dynamical systems, the Generalized Langevin Equation (GLE) has gained considerable popularity in recent years. Motivated by the question whether…

New exact completely closed homogeneous Generalized Master Equations (GMEs), governing the evolution in time of equilibrium two-time correlation functions for dynamic variables of a subsystem of s particles (s<N) selected from N>>1…

Probably one of the most striking examples of the close connections between global optimization processes and statistical physics is the simulated annealing method, inspired by the famous Monte Carlo algorithm devised by Metropolis et al.…

Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct…

We propose a methodology to generate hybrid machine learning models for the potential energy surface trained simultaneously on data from ab initio electronic structure calculations and on thermodynamic and/or structural observables from…

We present a general framework for the efficient simulation of realistic fermionic systems with modern machine learning inspired representations of quantum many-body states, towards a universal tool for ab initio electronic structure. These…

The properties of molecules and materials containing light nuclei are affected by their quantum mechanical nature. Modelling these quantum nuclear effects accurately requires computationally demanding path integral techniques. Considerable…

We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…

For multivariate co-generation in scientific applications, we advocate pairwise block rather than joint modeling of all variables. This design mitigates the computational burden and data imbalance. To this end, we propose an Annealed…

A diffusive trajectory drawn by the generalized Langevin equation (GLE) for a colloidal particle evokes a random fractal of a static polymer configuration. This article proposes a static GLE-like description that enables the generation of a…

Machine learning methods have nowadays become easy-to-use tools for constructing high-dimensional interatomic potentials with ab initio accuracy. Although machine learned interatomic potentials are generally orders of magnitude faster than…

Despite rapid progress in large language models (LLMs), the statistical structure of their weights, activations, and gradients-and its implications for initialization, training dynamics, and efficiency-remains largely unexplored. We…

Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among…

Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…

Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…

Coarse-grained (CG) models provide an effective route to reducing the complexity of molecular simulations (MD), but conventional approaches depend heavily on long all-atom MD trajectories to adequately sample configurational space. This…

Often in machine learning, data are collected as a combination of multiple conditions, e.g., the voice recordings of multiple persons, each labeled with an ID. How could we build a model that captures the latent information related to these…

We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary…

Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…

We present in detail the recently derived ab-initio molecular dynamics (AIMD) formalism [Phys. Rev. Lett. 101 096403 (2008)], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of…